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Proof step 3 from proof restn-last (previous step)

n ≤ # x0, ∀ n. n < # x0 → restn(n, x0).last = x0.last ⊦ restn(n, a ' + x0).last = (a ' + x0).last

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 4:
n ≤ # x0, ∀ n. n < # x0 → restn(n, x0).last = x0.last ⊦ x0 = [], restn(n, a ' + x0).last = (a ' + x0).last

Rule argument

fma: x0 = []

Additional information

Used simplifier rules: restN-zero: ⊦ restn(0, x) = x;%app: ⊦ x + [] = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%l: ⊦ a '.last = a; from specification list-last%size-01: ⊦ # [] = 0; from specification list-data%lez-01: ⊦ m ≤ 0 ↔ m = 0; from specification nat%zero-01: ⊦ ¬ m < 0; from specification nat-basic1 Used formulas: x0 = []